Revisiting Formal Copper(III) Complexes: Bridging Perspectives with Quasi‐d 10 Configurations

Abstract The formal Cu(III) complex [Cu(CF3)4]1− has often served as a paradigmatic example of challenging oxidation state assignment – with many reports proposing conflicting descriptions. Here we report a computational analysis of this compound, employing Energy Decomposition Analysis and Intrinsic Bond Orbital Analysis. We present a quasi‐d 10 perspective of the metal centre, resulting from ambiguities in d‐electron counting. The implications for describing reactions which undergo oxidation state changes, such as the formal reductive elimination from the analogous [Cu(CF3)3(CH2Ph)]1− complex (Paeth et al. J. Am. Chem. Soc. 2019, 141, 3153), are probed. Electron flow analysis finds that the changes in electronic structure may be understood as a quasi‐d 10 to d 10 transition at the metal centre, rendering this process essentially redox neutral. This is reminiscent of a previously studied formal Ni(IV) complex (Steen et al., Angew. Chem. Int. Ed. 2019, 58, 13133–13139), and indicates that our description of electronic structure has implications for the understanding of elementary organometallic reaction steps.

The electronic structures used for the electron flow analyses were obtained via single point energy calculations performed on the NEB geometries using the PBE0 functional [3] and the def2-TZVPP basis set. [4] The resolution of identity approximation (RIJCOSX) [5] was employed in conjunction with Weigend's universal fitting basis set (def2/J), [6] also with a fine integration grid (Grid5 NoFinalGrid) and an energetic convergence criterion of 10 -8 Hartree (TightSCF). Localization and visualization of the IBOs and virtual valence (vv-)IBOs was performed in an unreleased version of IboView (v2018). [7] All orbitals isosurfaces are shown such that 80% of the corresponding electron density is enclosed.
The NEB-CI implementation in ORCA [10] ensures the optimized reaction path well approximates the minimum energy path between the RE reactant [Cu(CF3)3(CH2Ph)] 1and the RE product complex [Cu(CF3)2•(CF3CH2Ph)] 1-. This is confirmed by using the converged climbing image (the highest energy structure from the NEB reaction path, RE-CI) as input for a transition state optimization (OptTS), which easily converged to an optimized saddle point (RE-TS) with a single imaginary frequency of -260.90 cm -1 (corresponding to F3C-CCH2Ph bond formation) and a B97-3c Gibbs free energy (G) of 27.7 kcal mol -1 , relative to the RE reactant [Cu(CF3)3(CH2Ph)] 1-, close to GRE-CI (32.3 kcal mol -1 ). The all-atom root mean squared deviation of RE-CI and RE-TS is 0.92 Å and the partially formed bond (F3C-CCH2Ph) distances are 2.05 and 2.07 Å, respectively.

Energy Decomposition Analysis
To further probe the electronic structure, and in particular the Cu d-configuration, Morokuma-Ziegler Energy Decomposition Analysis (EDA) [11] was performed in the Amsterdam Density Functional (ADF) suite of the AMS 2020 package. [12] These calculations were performed at the B97-3c optimized n=1 geometry from ORCA, and employed the PBE0 functional [3] in combination with the triple-ζ TZ2P basis set. [13] No frozen core approximation was made. Scalar relativistic effects were given via a ZORA Hamiltonian. [14] Numerical quality was defined with the Good keyword. For each EDA calculation only two fragments were defined: 1) the metal centre, Cu n+ and 2) the entire remaining ligand framework (CF3)4 (n+1)-. The optimised coordinates were reoriented such that the Cu-CF3 bonds lay along the xy axes, providing optimal overlap between the ligand and metal (3dx2-y2) orbitals. Although no symmetry was enforced during the complex and ligand calculations, local D4h symmetry was applied to the metal fragment to enable specification of the 4s 0 3d 8 , 4s 0 3d 9 and 4s 1 3d 10 electronic configuration via the IrrepOccupations keyword.

Energy Decomposition Analysis [Cu(CF3)4] 1-
To further probe the electronic structure of [Cu(CF3)4] 1-, and in particular the Cu d configuration, Morokuma-Ziegler Energy Decomposition Analysis (EDA) [11] was performed in the Amsterdam Density Functional (ADF) suite of the AMS 2020 package. [12] These calculations were performed at the B97-3c optimised n=1 geometry from ORCA (please see 'Computational details' above for more details), and employed the PBE0 functional [3] in combination with the triple-ζ TZ2P basis set. [13] No frozen core approximation was made. Scalar relativistic effects were given via a ZORA Hamiltonian. [14] Numerical quality was defined with the Good keyword. For each EDA calculation only two fragments were defined: 1) the metal centre, Cu n+ and 2) the entire united ligand framework [(CF3)4] (n+1)-.  Table S1).
EDA calculations require specification of the fragments comprising a molecule as input.
We chose to fragment [Cu(CF3)4] 1-into ligand and metal ( Figure S2, centre and right, respectively). D4h symmetry (an approximate point group of the pseudo square planar complex) was imposed on the metal fragment to ensure alignment between the Cu-C bonding axes and the lobes of the Cu 3dx2-y2 orbital, whose occupations was controlled via the Irrepoccupations keyword. The Cu atom defined the origin of the new axes. No symmetry was imposed during the ligand fragment and full complex calculations. The various Cu configurations were specified by changing the fragment charges, spins, and orbital occupations, as summarized in Table S1. For all entries with a non-zero number of unpaired S5

EOS
The Effective Oxidative State (EOS) method, [17] developed by P. Salvador and co-workers in 2015 allows for OSs to be determined from calculated wavefunctions. It employs the topological fuzzy Voronoi cells (TFVC), [18] which efficiently approximate Bader's topological basins from the Quantum Theory of Atoms in Molecules, [19] in order to partition the molecular space into atomic regions. Once an optimized geometry is obtained and a wavefunction is computed, the EOS of each of the fragments chosen by the user is computed, along with a reliability index, R, that formally ranges from 0-100%, R=50% indicates degeneracy of two assignments and R<50% indicates "that the assignation of the electrons has not followed an aufbau principle". [17] The R value allows the user to try different fragmentation schemes to see which is more appropriate for a given system. Gimferrer et al. reported the EOS of Cu in [Cu(CF3)4]to be +3, with R=51.7%, [20] at the ωB97X-V [21] /def2-TZVP [4] level of theory. The EOSs of copper at our chosen level of theory, PBE0/def2-TZVPP//B97-3c, are shown for several fragmentation schemes (Table S3). We note that our results agree closely with Gimferrer et al. only if each -CF3 moiety is treated as a separate fragment (entry 4). This fragmentation scheme seems to bias EOS(Cu) towards +3, perhaps because each -CF3 moiety cannot accept half an electron, as is necessary to agree with Snyder's original d 10 Cu(I) assignment. If, instead, all four trifluormethyl groups are treated as a united ligand framework (entry 1), EOS(Cu) = +1 with a greatly increased reliability index (R=85.2%). The sensitivity of EOS(Cu) to the choice of fragmentation scheme demonstrates, once again, the ambiguity of copper's OS in this molecule and the need for greater flexibility in our understanding of its electronic structure.

LOBA
In the same work, Gimferrer et al. [20] also compute the oxidation state of Cu in [Cu(CF3)4] 1within the Localised Orbital Bonding Analysis (LOBA) scheme, [22] developed by Head-Gordon an co-workers. Their result, Cu(III), obtained again at the ωB97X-V/def2-TZVP level of theory, agrees with our calculations performed at the PBE0/def2-TZVPP//B97-3c level. LOBA requires specification of a localization scheme, a method for the population analysis, a method for the orbital compositions and a percentage threshold to assign electrons of localized orbitals to atomic centres. We chose to use Pipek-Mezey localized orbitals, [23] a Mulliken population analysis, [24] the Hirshfeld method for the orbital compositions, [25] as implemented in the opensource program Multiwfn 3.7. [26] A threshold of 50% was specified. The same level of theory was use as our other calculations (PBE0/def2-TZVPP//B97-3c) calculated in Gaussian 16, Revision B.01, [27] using the PBE1PBE keyword and the basis set specified manually using the Basis Set Exchange. [28]

EOS of the formal reductive elimination from [Cu(CF3)3(CH2Ph)] 1-
The electron flow analysis of the reductive elimination from [Cu(CF3)3(CH2Ph)] 1- (Figure 3), reported by Paeth et al., [29] can be complemented by the application of the Effective Oxidation State (EOS) [17] approach from P. Salvador and co-workers (briefly discussed above). The results (Table S4) show that EOS(Cu) = +1 throughout the reaction, with a reliability index of R=58% for the RE reactant [Cu(CF3)3(CH2Ph)] 1and R=(63%, 100%) for the RE product complex [Cu(CF3)2•(CF3CH2Ph)] 1-(depending on if the trifluoroethyl benzene moiety is treated a single fragment). This parallels our previous observations that EOS(Ni) remained constant throughout a formal reductive elimination, [30] and further justifies consideration of such reactions as effectively redox neutral. Figure S4: Chosen fragments for a) the reactant and b-c) the product of the reductive elimination from a formal Cu(III) centre (Figure 3c), reported by Paeth et al. [29]